Interesting conversation! A lovely little set you have there, and others have shown some very nice glass as well. Engraved glass is my thang, and it's nice to see a long thread about it. Haven't been around for a while.
Glass definitions are so tough because they're so variable. Take "rock crystal." Originally it referred to a style of deep engraving that covered much of the surface of a piece and was entirely polished, as others have indicated. I guess that's still true in the UK, but over here it has been used differently, so that some companies came to call all entirely polished patterns, rock crystal. Libby had a line of stemware called Rock Crystal, though the engraving is nothing like what was originally meant by the term.
Intaglio has always been a tough one to pin down - it seems like everyone has their own definition. Based on a keen interest and resulting research, to me intaglio can in general be described as deep engraving, usually done with a stone or diamond wheel, followed by copper wheel engraved detail. There isn't always a clear distinction, but generally if a design is engraved entirely with a copper wheel it's probably not intaglio. The engraving in the OP I wouldn't consider intaglio. This could be another geographic difference, but Hajdamach also describes intaglio as being stone cut. He doesn't say anything about copper wheel details, but they were certainly added to a lot of what is now known as intaglio, which includes a lot more than the type of pieces he discusses (in the 1800-1924 book).
Someone said this was marked as being made in England, but I didn't see where Flying Free said that. Is it the case or not? That design could easily have been done by Hawkes, Sinclaire, or the like (it's not Pairpoint as far as I can tell). It looks quite familiar, actually. Is either piece marked? Some American etched sigs are very very hard to see.